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  • Level: GCSE
  • Subject: Maths
  • Word count: 5692

Statistics "Mayfield high school" - the taller the person the more they weigh.

Extracts from this document...

Introduction

Raheem Mirza                Mathematic Coursework

Candidate No : 2149

MATHS COURSEWORK

STATISTICS

“MAYFIELD HIGH SCHOOL”

STUDENT: RAHEEM MIRZA

TEACHER: MS LEWIS


Part 1: Introduction/Aim

I imagine that the taller the person is the more they weigh, due to body mass. I also assume that the gender doesn’t have an effect on their height and weight. I will try and prove or disprove this in my investigation. I will take people from Key Stage 3.

Part 2: Method:

Using Microsoft Excel, i selected 40 random people from the Mayfield High School database. I chose to use the formula =SUM ()*40. This automatically gave me 40 students which are below.  

Part 3: My 40 Random Result

Random Result

Number

Year Group

Gender

Height

(cm)

Weight

(kg)

671

1

9

Female

159

50

687

2

9

Female

156

50

261

3

7

Male

156

39

342

4

8

Female

175

64

584

5

9

Female

180

82

445

6

8

Male

167

51

388

7

8

Female

180

58

428

8

8

Male

154

37

646

9

9

Female

165

52

291

10

8

Female

168

59

224

11

7

Male

148

26

309

12

8

Female

163

42

654

13

9

Female

165

49

469

14

8

Male

165

40

262

15

7

Male

149

35

353

16

8

Female

160

46

635

17

9

Female

160

40

804

18

9

Male

180

42

685

19

9

Female

152

50

388

20

8

Female

180

58

479

21

8

Male

168

51

75

22

7

Female

166

45

94

23

7

Female

173

51

552

24

9

Female

160

60

548

25

8

Male

152

45

468

26

8

Male

182

54

238

27

7

Male

160

40

630

28

9

Female

162

41

750

29

9

Male

180

55

258

30

7

Male

157

48

271

31

7

Male

151

39

560

32

9

Female

152

46

739

33

9

Male

160

68

792

34

9

Male

170

50

416

35

8

Male

148

40

684

36

9

Female

158

55

335

37

8

Female

175

55

430

38

8

Male

162

53

176

39

7

Male

152

32

470

40

8

Male

165

59

Types of Formulae

I will use the following types of formulae;

  • Quartile Ranges
  • Mean, Mode, Median and Range
  • Pearson’s Product Moment Correlation Co-Efficient

To represent my data, I intend to use the following types of Graphs;

  • Cumulative Frequency Graphs
  • Histograms
  • Frequency Polygons
  • Box and Whisker Plots

Part 5:

I will now work out the mean, mode, range and median of the data. I have decided to use intervals because height and weight are continuous data.

Frequency table for height of boy’s and girls

Height Interval

Tally

Frequency (f)

Midpoint (x)

f (x)

148 – 154

9

151

1359

155 – 161

10

158

1580

162 – 168

11

135

1485

169 – 175

4

172

688

176 – 182

6

179

1074

Total:

∑f=40

x=795

fx=6188

Mean: 6188/40 = 154.7

Mode Interval: 162 – 168

Median: 162 – 168

Range: 182 – 148 =34

Frequency table for weights of boy’s and girls

Weight Interval

Tally

Frequency (f)

Midpoint (x)

f (x)

26 –32

2

29

58

33 – 39

4

36

144

40 – 46

11

43

473

47 – 53

11

50

550

54 – 60

8

57

456

61 – 67

2

64

128

68 – 74

1

71

71

75 – 81

0

78

0

82 – 88

1

85

85

Total:

∑f=40

∑x=513

fx=1965

Mean: 1965/40 =49.13    2dp

Modal Interval: 40 – 46 and 47 – 53

Median: 47 – 53

Range: 82 – 26 =56

Part 6: PMCC for my 40 students

Random Result

Number

Height  (y)

(cm)

Weight  (x)

(kg)

xy

671

1

159

50

7950

687

2

156

50

7800

261

3

156

39

6084

342

4

175

64

11200

584

5

180

82

10440

445

6

167

51

5698

388

7

180

58

8580

428

8

154

37

9912

646

9

165

52

3848

291

10

168

59

6846

224

11

148

26

8085

309

12

163

42

6600

654

13

165

49

5215

469

14

165

40

7300

262

15

149

35

6400

353

16

160

46

7560

635

17

160

40

7600

804

18

180

42

10440

685

19

152

50

8568

388

20

180

58

7470

479

21

168

51

8823

75

22

166

45

7470

94

23

173

51

8823

552

24

160

60

9600

548

25

152

45

6840

468

26

182

54

11648

238

27

160

40

6400

630

28

162

41

6642

750

29

180

55

9900

258

30

157

48

7536

271

31

151

39

5889

560

32

152

46

6992

739

33

160

68

10880

792

34

170

50

8500

416

35

148

40

5920

684

36

158

55

8690

335

37

175

55

9625

430

38

162

53

8586

176

39

152

32

4864

470

40

165

59

9735

n=40            

y=1930                      

x=6527              

xy=318312

x² =1068757      y² =96454

Formulae for PMCC

The information for the following formulae is above, where the PMCC for the students is worked out.

...read more.

Middle

Tally

Frequency (f)

Midpoint (x)

F (x)

152 – 158

4

155

620

159 – 165

8

162

1296

166 – 172

2

169

338

173 – 179

3

176

528

180 - 186

3

183

549

Total:                  

f=20                    

x=845                

fx=3331

Mean:  3331/20 = 166.55

Mode: 159 – 165

Median: 159 – 165

Range: 180-152 =28

Group frequency table for the height of boy’s

Height

Tally

Frequency (f)

Midpoint (x)

F (x)

148 – 154

7

151

1057

155 – 161

4

158

632

162 – 168

5

165

825

169 – 175

1

172

172

176 – 182

3

179

537

Total:                                    

f=20

x=825                

fx=3223

Mean: 3223/20 = 161.15

Mode: 148 – 154

Median: 155 – 161

Range: 182 – 148 =34

Group frequency table for weight of girl’s

Weight (kg)

Tally

Frequency (f)

Midpoint (x)

F (x)

40 – 46

6

43

258

47 – 53

6

50

300

54 – 60

6

57

342

61 – 67

1

64

64

68 – 74

0

71

0

75 – 81

0

78

0

82 - 88

1

85

85

Total:

f=20

x=448

fx=1049

Mean:  1049/20 =52045

Mode:  40 – 46, 47 – 53 and 54 – 60

Median:  47 – 53

Range: 82 –40 =42

Group frequency table for weight of boy’s

Weight (kg)

Tally

Frequency (f)

Midpoint (x)

F (x)

26 – 32

2

29

58

33 – 39

4

36

160

40 – 46

5

43

215

47 – 53

5

50

250

54 – 60

2

57

114

61 – 67

1

64

64

68 - 74

1

71

71

Total:

f=20

x=350

fx=932

Mean: 932/20 = 46.6

Mode: 40 – 46 and 47 – 53

Median: 40 – 46

Range: 68 – 26 =42


Part 9: PMCC for height and weight for females

Number

Height (y)

(cm)

Weight (x)

(kg)

xy

1

159

50

7950

2

156

50

7800

3

175

64

11200

4

180

82

14760

5

180

58

10440

6

165

52

8580

7

168

59

9912

8

163

42

6846

9

165

49

8085

10

160

46

7360

11

160

40

6400

12

152

50

7600

13

180

58

10440

14

166

45

7470

15

173

51

8823

16

160

60

9600

17

162

41

6642

18

152

46

6992

19

158

55

5690

20

175

55

9625

   n=20              

y=1053                

x=3309                  

xy=14818

x²=549011            y²=57187

Sxx =549011 – 3309 ²/20 =1536.95

Syy =57187 – 1053²/20 =1746.55

Sxy =175215 – 3309*1053/20 =996.15

r =996.15/1746.55*1536.95 =996.15/1638.401667 =0.6

Part 10: PMCC for male height and weight

Number

Height (y)

(cm)

Weight (x)

(kg)

xy

1

156

39

6084

2

167

51

8517

3

154

37

5698

4

148

26

3848

5

165

40

6600

6

149

35

5215

7

180

42

7560

8

168

51

8568

9

152

45

6840

10

182

64

11648

11

160

40

6400

12

180

55

9900

13

157

48

7536

14

151

39

5889

15

160

68

10880

16

170

50

8500

17

148

40

5920

18

162

53

8586

19

152

32

4864

20

165

59

9735

n =20                        

y =3226                      

x =914

∑xy =4140

x²=522550                     y²=43966

Sxx =522550 – 3226²/20 =2196.2

Syy =43966 – 914²/20 =2196.2

Sxy =148818 – 3226*914/2196.2 =1389.8

r = 1389.8/2196.2*2196.2 =1389.8/2196.2 =0.6

Part 13:

Now I will find the equation of the line of best fit in all three scatter graphs.

Equation of the line of scatter graph 1 considering the point’s A and B.

All of my samples

A =(65,178)

B =(33.5,150)

Gradient =(y2 – y1)/(x2  - x1)

              =178-150/65-33.5

              =8/9

y =8/9x + c

Intercept (c) using co-ordinate (65,178)

178 =(8/9*65) + c

178 =(57078) + c

c =120.22                     2dp

Equation of line of scatter graph 1

y =8/9x + 120.22

h =8/9w + 120.22

Were h =height and w =weight


Equation of line scatter graph 2 considering point’s A and B

Boys Sample

A =(55,178)

B =(34.5,140)

Gradient =(y2 – y1)/(x2  - x1)

               =178 – 140/55 – 34.5

               =76/41

y =76/41x + c

Intercept (c) using co-ordinate (55,178)

178 =(76/41*55) + c                                     2dp

178 – 101.95 + c

c =76.05                                                      2dp

Equation of the line of scatter graph 2

y =76/41x + 76.05

h =76/41w + 76.05

Were h =height and w =weight


Equation of the line of scatter graph 3 considering point’s A and B

Girls Sample

A =(80,180)

B =(40.5,160)

Gradient =(y2 – y1)/(x2  - x1)

               =180 – 160/80 – 40.5

               =40/79

y =40/79x + c

Intercept (c) using co-ordinate (80,180)

180 =(40/79*80) + c

180 – 40.51 = c

c =139.49                                                     2dp

Equation of the line of scatter graph 3

y =40/79x + 139.49

h =40/79w + 139.49

Were h =height and w =weight

Now I will explain how the equation of the best-fit line can be used. If the weight is known of a student then the height can be estimated using the equation. Also if the height is known the weight can be estimated.


Using my found Formulae(s)

Example 1

Using the line of scatter graph 3 (girls)

h =40/79w + 139.49

The weight of a female student is 82 kg. The height can be estimated using the equation.

h =(40/79) + 139.49

h =41.51 + 139.49

h =181.01                         2dp

Example 2

The height of a female student is 180 cm. The weight can be estimated using the equation.

h =40/79w + 139.49

180 =40/79w + 139.49

180 – 139.49 =40.51

w =40.51*70/40

w =70.89                          2dp

This suggests that if there was a male student with a height of 180 cm then his weight is estimated to be 70.893 3dp


Part 14: Cumulative Frequency

Table A

Cumulative frequency table for the height of girls

Height

Frequency

Cumulative Frequency

152 – 158

4

4

159 – 165

8

12

166 – 172

2

14

173 – 179

3

17

180 - 186

3

20

See Graph 1

Table B

Cumulative frequency table for the height of boys

Height

Frequency

Cumulative Frequency

148 – 154

7

7

155 – 161

4

11

162 – 168

5

16

169 – 175

1

17

176 – 182

3

20

See Graph 2

Table C

Cumulative frequency table for the weight of girls

Weight

Frequency

Cumulative Frequency

40 – 46

6

6

47 – 53

6

12

54 – 60

6

18

61 – 67

1

19

68 – 74

0

19

75 – 81

0

19

82 – 88

1

20

See Graph 3

Table D

Cumulative frequency table for the weight of boys

Weight

Frequency

Cumulative Frequency

26 – 32

2

2

33 – 39

4

6

40 – 46

5

11

47 – 53

5

16

54 – 60

2

18

61 – 67

1

19

68 – 74

1

20

...read more.

Conclusion

1.52

45

77

11

Female

1.59

42

78

11

Female

1.63

38

79

11

Female

1.62

38

80

11

Female

1.70

60

81

11

Female

1.58

48

82

9

Male

1.60

60

83

9

Male

1.56

60

84

9

Male

1.66

54

85

9

Male

1.66

70

86

9

Male

1.52

52

87

9

Male

1.75

75

88

9

Male

1.65

45

89

9

Male

1.52

54

90

9

Male

1.67

54

91

9

Male

1.71

60

92

9

Male

1.80

48

93

9

Male

1.73

66

94

9

Male

1.55

50

95

9

Male

1.77

66

96

9

Male

1.73

52

97

9

Male

1.54

44

98

9

Male

1.47

42

99

9

Male

1.75

63

100

9

Male

1.62

40

101

9

Male

1.46

45

102

9

Male

1.80

64

103

9

Male

1.50

70

104

9

Male

1.61

38

105

9

Male

1.54

60

106

9

Male

1.55

51

107

7

Male

1.49

47

108

7

Male

1.48

47

109

7

Male

1.63

60

110

7

Male

1.50

40

111

7

Male

1.53

35

112

7

Male

1.54

48

113

7

Male

1.54

51.5

114

7

Male

1.48

26

115

7

Male

1.61

56

116

7

Male

1.65

41

117

7

Male

1.30

35

118

7

Male

1.61

56

119

7

Male

1.47

47

120

7

Male

1.67

60

121

7

Male

1.61

46

122

7

Male

1.50

51

123

7

Male

1.47

45

124

7

Male

1.67

53

125

7

Male

1.50

56

126

7

Male

1.52

45

127

7

Male

1.63

60

128

7

Male

1.43

41

129

7

Male

1.45

31

130

7

Male

1.58

48

131

7

Male

1.60

40

132

7

Male

1.65

35

133

7

Male

1.63

50

134

11

Male

1.94

80

135

11

Male

1.69

65

136

11

Male

1.67

60

137

11

Male

1.5

35

138

11

Male

1.86

80

139

11

Male

1.68

63

140

11

Male

1.68

63

141

11

Male

1.83

75

142

11

Male

1.68

56

143

11

Male

1.65

47

144

11

Male

1.62

92

145

11

Male

1.8

68

146

11

Male

1.68

58

147

11

Male

1.71

54

148

11

Male

1.7

56

149

11

Male

1.62

50

150

11

Male

1.71

57


image02.png

From the graph we can see there is a strong positive correlation. However to use a statistical way to prove this I will use the Pearson’s Product Moment Correlation Co-Efficient. I have discovered a key in excel which automatically does this calculation without making conscious though.

Below is a guide to use of this control;

image03.png

image00.pngimage01.png

This then brings up a screen, I then pressed on ‘Pearson’s’, this automatically brings up the PMCC of the sample.

Product Moment Correlation Co-Efficient of height and weight of boys and girls was calculated to be 0.568279. This means it is a “Moderate Correlation”.

Now I will create a scatter graph of male students which are inclusive in my sample. This can be viewed below;

image04.png

Similarly, as for this graph from the naked eye the graph seems to be positively correlated. But using Pearson’s Product Moment Correlation Co-Efficient, we will see how much it is correlated, the formulae accessible to us tells us the PMCC between height and weight of boys is 0.639816. This again shows us it is a‘Moderate Correlation’.

Now I will create a scatter graph of female students which are inclusive in my sample. This can be viewed below;

image05.png

This graph doesn’t really have a correlation to it but using PMCC the correlation is 0.483991. This again is a Moderate correlation.

Extension conclusion

In my initial conclusion, I stated girls were generally heavier than boys. The conclusion which I have come to now is the same as my initial hypothesis. Boys are generally heavier than girls.

-  -

...read more.

This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

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    This shows us that females live longer than males. countries male female money Austria 76 81.89 $30,000 Czech republic 77.52 79.24 $15,700 France 75.8 83.27 $27,600 Liechtenstein 75.8 83.02 $25,000 Macedonia 72.45 77.2 $6,700 Malta 76.51 80.98 $17,700 Moldova 60.88 69.39 $1,800 Romania 67.63 73.27 $7,000 San Marino 78.02 85.34 $34,600 Sweden 78.12 82.62 $26,800 South America These graphs

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